Learning pack · IGCSE handout

Similar Shapes 2

What's in this pack: printable worksheet PDF, matching answers PDF (IGCSE / Secure–Stretch practice). Similarity scales lengths by $k$ , areas by $k^2$ , volumes by $k^3$ . Matching angles and proportional sides define similarity.

Resources at the top · full summary · videos with short notes below.

🎒 Resources in this pack

Jump straight to the printable files, or scroll to the summary and videos.

Scaffolded Learning Sheet — attempt the worksheet, then use the Answers for a full written solution.

📝 Open Learning Sheet ✅ Open answers 🎬 More topic videos (6)📖 Full summary

Files: 36_similar_shapes_2_handout.pdf · 36_similar_shapes_2_handout_answers.pdf

Full topic summary

Similarity scales lengths by $k$ , areas by $k^2$ , volumes by $k^3$ . Matching angles and proportional sides define similarity.

Key learning points

Corresponding angles equal; corresponding sides in the same ratio.
Area factor $=(\text{length factor})^2$ ; volume factor cubed.
Find missing sides with matching vertices carefully labelled.

Worked example 1 — Area scale factor

Length SF $k=3$ . Area SF?

Working

9

Square $k$ .

Worked example 2 — Volume scale factor

Length SF $k=2$ . Volume SF?

Working

8

Cube $k$ .

Worked example 3 — Length from areas

Areas ratio $16:9$ . Length SF?

Working

4:3

Square-root of area SF.

Worked example 4 — Find length from areas

Similar shapes; areas $36$ and $16$ . Length scale factor?

Working

k=\sqrt{36/16}=3/2

Length SF is the square root of the area SF.

🎬 Topic videos

Beautiful Trigonometry - Numberphile
Numberphile · 12 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
The Cosine Rule (1 of 3: Proof of the Formula)
Eddie Woo · 13 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Similar Figures
Eddie Woo · 12 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Congruent Figures (1 of 2: Introduction)
Eddie Woo · 8 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Trigonometry Introduction - Corbettmaths
Corbettmaths · 6 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
SOHCAHTOA Finding a missing length
Maths Genie · 10 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.

More Lower Secondary packs

Browse the hub Learning Packs & Summary, or open the compact Similar Shapes 2 summary.